®γσ, Eng Lian Hu

白戸則道：悟空がやらなきゃ誰がやる！

Betting Strategy and Model Validation

Abstract

This is an academic research by apply R statistics analysis to an agency A of an existing betting consultancy firm A. According to the Dixon and Pope (2003), due to business confidential and privacy I am also using agency A and firm A in this paper. The purpose of the anaysis is measure the staking model of the firm A. For more sample which using R for Soccer Betting see http://rpubs.com/englianhu. Here is the references of rmarkdown and An Introduction to R Markdown. You are welcome to read the Wrangling F1 Data With R if you are getting interest to write a data analysis on Sports-book.

1. Introduction to the Betting Stategics

1.1 Introducing Betting Strategies

As a player, we know gambling is that an activities which bet against bankers. Normally gamblers applied few betting strategies to make money from bankers or may be other players. You can try to refer to ??????????????????R???Python - Data Science is the art of turning data into actions - ?????????21?????????????????????or Betting Strategy for more information.

Well, I’ll introducing some sports betting strategies used by a company Sports Insights (You can just read as your own reference, since I’ve never subscribe thier service, here I term it as SI) might help you improve your winning percentage and start making money investing in sports. The following concepts represent some of the most lucrative historical betting trends and are the same tools used by sharp bettors to turn consistent profits.

Betting Against the Public is one of the most popular and simplest methods used by SI to maximize value in the sports betting marketplace.

SI will show how analyzing betting trends data and line movement can help you identify which games the sharp money (wagers placed by sharps, wiseguys or betting syndicates) is taking.

SI’s major line move analysis explains how to interpret line moves across the sports betting marketplace in order to find value.

This article explains how sportsbooks shade their lines to exploit human tendencies and how you can take advantage by using SI’s Betting Against the Public strategy.

Shopping for the best possible number is an easy way to improve your winning percentage over the course of an entire season.

Understanding the importance of units won vs winning percentage will help you evaluate the true worth of any sports betting system.

Here is some websites or companies which provides sportsbook trading/betting.

-Sports Betting Tips For Profit

[16]Maurizio Montone (2015) taking 82 operators’ as sample data for research on arbitrages and bookmakers’ characteristics. [17]Steven D. Levitt (2004) analyse the betslips breakdown which is similar with section 3 in this paper.

1.2 Value Betting

Section 1.1 Introducing Betting Strategies describe some basic concepts about betting strategies. Now we focus on Value betting and it is the popular and efficient staking strategy since money management is the key for betting strategy.

  It's not a matter of life or death. But if that team, that result or that referee's decision goes against them, the lives of their wives and their children are affected. The mortgage does not get paid. Holidays are cancelled. They are not players or managers. They are football's professional gamblers.

  It is their full-time job to win money betting on the game. There are not many successful enough to survive. It is estimated, by the gamblers interviewed here, that fewer than 3 percent of gamblers who have what it takes to "go pro" can earn a living from betting.

  No wonder they are a secretive, paranoid bunch. Never do they reveal exactly how they win their money or how much. Their greatest secret is what is known as "the edge". That nugget of information which tells them that the odds on the football betting market is wrong. Only then do they hand over their hard-won dough.

  It takes hours of eye-bleeding research to find "the edge". Most pros spend hours, and thousands of pounds, building statistical models. Others will employ specialists—analysts and statisticians—to build a complex algorithm for them. If successful enough, they will attract wealthy investors who will hand over thousands, sometimes millions, to bet for them and be promised a healthy return.

  Tony Bloom, a legendary gambler known as "The Lizard" is one such operator. So revered, Bloom runs Star Lizard, a company that employs a raft of people to analyse football matches for his millionaire-only investors. Bloom is rumoured to be worth more than £1 billion and owns Brighton, the Premier League wannabes.

source : Mugs and Millionaires: Inside the Murky World of Professional Football Gambling

The best and the most successful punters are money managers looking for ideal situations, which are defined as matches with only high percentage of return. In individual situations luck will play into the outcome of an event, which no amount of odds compiling can overcome, but in the long run a disciplined punter will win more of those lucky games than lose.

1.3 Professional Gambler

Nowadays, operates make a lot of restriction to increase their profits. For example: single bet maximum stakes per account, triggers upon staking per bet, single match maximum stakes per account, vigorous/spreads margin (Which will describe in 2.2 Overrounds / Vigorish). As a professional gambler we are require a high level mathematical skill in order to take profit from operators. Below are some articles about sports betting data analysis. - Play Data, Play Ball!Exploring Baseball Data with R - openWAR - How Predictable is the English Premier League? - It’s boffins versus bookies on the World Cup Rankings

As we know George Soros and Jim Rogers are two of most successness punters in financial market while they used to analyse more than 25 companies from financial reports and also their business when they was working in Atom fund. Environment and the life of punters. - Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field - How hedge funds work - Rob Mastrodomenico uses data to estimate the outcomes of sports events for professional punters, and it’s a complicated business - ATASS - Work to have fun - ??????????????????????????????????????? - ???????????????:????????????156???????????????????????????“????????????”???

Now that you have some basic betting strategy knowledge and concept, you can try to learn further sportsbook staking modelling to take the challenge.

2. Data

2.1 Collect and Reprocess the Data

I collect the data-set of World Wide soccer matches from year 2011 until 2015 from a British betting consultancy named firm A. All bets placed by display on HK currency, and the odds price also measure based on Hong Kong price.

I tried to apply RSelenium on RStudio Server Centos7 to scrape the data from live-score website includes the odds price but the binary phantomjs is not available for Linux, and I also not familiar with the installation of Java as well as setting of the path for rJava. Kindly refer to Natural Language Analysis for more information about the teams name matching.

table 2.1.1 : 48640 x 43 : Sample data collected for the research.

  About 90 percent of money wagered will be on the Asian handicap, a market that allows the team expected to win a "head start" of a quarter of a goal or more to the opposition. The rest of the money staked will go on a market for over or under a certain number of goals and the match-result market.

source : Mugs and Millionaires: Inside the Murky World of Professional Football Gambling

In order to analyse the AHOU, here I’ve filtered out all soccer matches other than AHOU which is the table showing above (For example : Corners, Total League Goals etc.) for whole research paper. Please refer to Natural Language Analysis to see the firm A staking raw data-set.

You are feel free to read Asian Handicap and Arbitrage of Synthetic Asian Handicap Bets for some basic lession about Asian Handicap Bets.

2.2 Overrounds / Vigorish

Fair odds: the odds that would be offered if the sum of the probabilities for all possible outcomes were exactly 1 (100%). For example, supposing we had a market with three possible outcomes {A, B, C} with probabilities of success \(P(A) = 0.5, P(B) = 0.4\) and \(P(C) = 0.1\), the fair odds would be 2.00, 2.50, and 10.00 respectively, which are just the inverse of the estimated probabilities.

Overround: Also called vigorish (or vig for short) in American sports betting, the over-round is a measure of the bookmaker’s edge over the gambler. The bookmaker will never offer fair odds on a market. In practice, the payout offered on each selection will be reduced, which in turn increases the reflected probability of an event. When odds have been adjusted in this way the sum of the probabilities for all events will exceed 1 (100%). The over-round is the amount by which the sum of all probabilities exceeds 100% and it is the bookmaker’s profit margin.

For example, if we had a market with two possible outcomes {A, B}, where \(P(A) = P(B) = 0.5\), the fair odds on each selection would be 2.00. However, the bookmaker may offer payouts of 1.85 on each selection. The corresponding probabilities for each selection are now 1/1.85 = 0.5405405, and the sum of the probabilities for all outcomes is 0.5405405 x 2 = 1.0810811. The over-round is 8.1%, and for every $100 paid out by gamblers the bookmaker expects to make a profit of 8.1 dollars, assuming that there are balanced bets on both A and B.

I just simply get the lay price by applying below equation.

\[P_i^{HK_{Lay}} = 1/P_i^{HK_{Back}}-\nu_{j}\] equation 2.2.1

While \(\nu\) is the vigorish and \(j={1,2}\) which are AH=0.1 and OU=0.1. I have just simply calculated the Layed Fair odds (Odds Price with Vigorish which offer by operators), here I apply a setting profile which is term as lProfile (you can casually edit the soccer match profile setting) to get the Real Odds (Net Odds Price without Vigorish). As well as the Value \(Value = Real Price/Fair Odds\). Here we can use the Bet Stake Calculator Kelly Staking Calculator. I simply reverse value \(\Re\) to get the estimated \(P_{i}^{EM}\) (firm A) where we will talk in Section [4.1 Linear Model] and later [4.3 Poisson Modelling] about odds modelling.

Table 2.2.1 : Sample Data of Virogish/Overrounds and Odds Price
No EUPrice HKPrice fHKPriceL fMYPriceB fMYPriceL netProbB netProbL
50 2.00 1.00 0.880 1.000 0.880 0.5319 0.4681
72 1.78 0.78 1.100 0.780 -0.909 0.4149 0.5851
122 2.11 1.11 0.781 -0.901 0.781 0.5870 0.4130
123 1.64 0.64 1.241 0.640 -0.806 0.3402 0.6598
164 1.97 0.97 0.910 0.970 0.910 0.5160 0.4840
219 1.92 0.92 0.980 0.920 0.980 0.4842 0.5158

table 2.2.1 : 48640 x 43 : Vigorish, price and probabilities sample table.

Above table 2.2.1 just provides some sample about the odds price and over-round while you can refer to table 2.1.1 for details. Meanwhile, you can know more details about the return of investment, convertion and also origin region based on same probabilities among different Odds Types/Styles via Betting Odds Converter or just simply google’ing.

3. Summarise the Staking Model

3.1 Summarise Diversified Periodic Stakes

Before we start analyse the staking model, we are firstly see some diversified periodic breakdown Stakes and Profit & Lose of the Agency A.

graph 3.1.1 : Investment Annual summary graph.

From the graph above showing that the investment of firm A through agency A generates a positive return (profit). Please refer to table 4.1.1 for more details about investment analysis.

table 3.1.1 : 55 x 16 : Investment monthly breakdown table.

From the table above, we realized that the Asian agency A make profit by follow the British sports betting consultancy firm A every year. Since thousands of bets (and maximum bet limit setting, league profile setting, and also value betting which properly based on Kelly model, mean value will be kinda bias) placed per month, here we take median will be accurate than mean value.

graph 3.1.2 : Investment monthly trend graph.

table 3.1.2 : 383 x 17 : Investment daily breakdown table.

graph 3.1.3 : Investment daily trend graph.

From the graph above, we can easily know the figure of Stakes, Returns and Profit & Lose while below table separate into daily breakdown. The table shows the daily stakes and also quantile values.

3.2 Summarise the Staking Handicap

table 3.2.1a : 30 x 18 : Asian Handicap - handicap breakdown table.

table 3.2.1b : 60 x 18 : Goal Line - handicap breakdown table.

Table 3.2.1c : Sample data about Handicap, Stakes and PL
HCap AHOU Stakes Return PL R.percent PL.percent
0.50 AH 134536.2 134138.0 -398.1590 0.9970% -0.0030%
-0.25 AH 157391.8 209674.0 52282.1525 1.3322% 0.3322%
0.25 AH 233920.2 235755.7 1835.4312 1.0078% 0.0078%
0.00 AH 262692.1 270381.5 7689.4210 1.0293% 0.0293%
3.00 OU 78662.0 79823.7 1161.6975 1.0148% 0.0148%
2.50 OU 79000.0 79756.0 756.0025 1.0096% 0.0096%
2.00 OU 104969.2 111165.0 6195.8041 1.0590% 0.0590%
2.25 OU 110072.4 132015.5 21943.1013 1.1994% 0.1994%

table 3.2.1c : 8 x 7 : Handicap, stakes and PL sample table.

From above tables, firm A mostly placed on Asian Handicap range concedes/taken 0 ball on agency A. Menwhile the odds -0.25 is most profitable from return rate.

Secondly, from the Goal Line mostly taking over selection on 2 balls. (Since Dutch, Japanese, Spanish and Women soccer leagues always scoring more goals, but Portuguese, Italian, French leagues always score less, English leagues average 2.5 balls)

graph 3.2.1a : Asian Handicap - handicap breakdown staking graph.

graph 3.2.1b : Goal Line - handicap breakdown staking graph.

Now we look at the graph above, we can know the Stakes breakdown on both AH and OU.

3.3 Summarise the Staking Prices

table 3.3.1a : 49 x 18 : Asian Handicap - price range breakdown table.

table 3.3.1b : 32 x 18 : Goal Line - price range breakdown table.

Table 3.3.1c : Sample data about Price Range, Stakes and PL
pHKRange pMYRange Stakes Return PL R.percent PL.percent
(0.6,0.7] (0.6,0.7] 123154.8 136124.8 12970.01 1.1053% 0.1053%
(1.1,1.2] (-0.9,-0.8] 126400.0 138462.0 12062.03 1.0954% 0.0954%
(0.7,0.8] (0.7,0.8] 278201.2 296874.7 18673.48 1.0671% 0.0671%
(1,1.1] (-1,-0.9] 354514.3 385962.6 31448.23 1.0887% 0.0887%
(0.8,0.9] (0.8,0.9] 460616.2 501271.2 40655.00 1.0883% 0.0883%
(0.9,1] (0.9,1] 496308.3 544973.5 48665.12 1.0981% 0.0981%

table 3.3.1c : 6 x 7 : Price range, stakes and PL sample table.

From above tables, the price range on (0.9,1] are mostly been placed. We try to compare the stakes between 0.70~0.80 and 1.10~1.20, 0.60~0.70 and 1.20~1.30 and the returns/profit, we will know the price is importance on Value Betting.

graph 3.3.1a : Asian Handicap - price range staking graph.

graph 3.3.1b : Goal Line - price range staking graph.

Above graph shows the Stakes and P&L on different price range in MY Odds style. In fact the MY Odds Style will be easier to count and understand in statistics as well as plot graph since the return (both won and lost) will be ONLY from -1 to 1 while HK/Europe Odds Style will count from -1 to Inf. However I keep both HKOdds and MYOdds Please refer to table 2.2.1 for more details.

However, due to consideration of the stakes amount, here I just simply use the HK in order to make the Stakes and Return/PL exactly same with the dataset.

3.4 Summarise the In-Play Staking Timing

table 3.4.1a : 27 x 18 : Asian Handicap - In-Play time range breakdown table.

table 3.4.1b : 23 x 18 : Goal Line - In-Play time range breakdown table.

The table above shows the breakdown stakes on Breaks includes pregames of Extra-Time (started 90 minutes games), Half-Time and Full-Time in both 90 minutes games and also Extra-Time, Injuries-Time, Breaks-Time etc (All stakes after blew game-start whistle and before final result). While No means pre-games stakes and P&L summary.

graph 3.4.1a : Asian Handicap - In-Play time range graph.

graph 3.4.1b : Goal Line - In-Play time range graph.

From the above graph shows the In-Play stakes, the first (0,10] time range placed most stakes while (55,60] start dropping. The <NA> includes all stakes when the soccer players are not playing on the football field. (Pre-games, Half-Time, Full-Time, Extra-Time, Injuries Time, Breaks Time etc.)

3.5 Summarise the In-Play Staking Based on Current Score

table 3.5.1a : 231 x 18 : Asian Handicap - In-Play state-space staking breakdown table.

table 3.5.1b : 341 x 18 : Goal Line - In-Play state-space staking breakdown table.

Above table shows a further details breakdown of In-Play stakes, includes the current scores and also current concedes/given handicap during In-Play while <NA> during Break means Break-Time or pre-Extra-Time etc. The complete data is dim(sample.data) 231 x 18 and 341 x 18 for both AH and OU.

graph 3.5.1a : Asian Handicap - In-Play state-space graph.

graph 3.5.1b : Goal Line - In-Play state-space graph.

Section 3 summarise breakdown tables and also graphs on the investment of firm A. Basically, soccer sports investment need to consider below criteria :

While the further linear model will also take above criteria for investment. You can also refer to my previous research which is Odds Modelling and Testing Inefficiency of Sports-Bookmakers.

4. Staking Model

4.1 Basic Equation

Before we start modelling, we look at the summary of investment return rates.

Table 4.1.1 : Annual Return of Investment. (’0,000)
Sess Stakes Return n rRates
2011 352953.2 380126.9 6441 1.076989
2012 425665.4 471305.4 10159 1.107220
2013 491434.3 529818.1 12494 1.078106
2014 464431.5 517768.0 12620 1.114843
2015 247873.0 264508.0 6926 1.067111

table 4.1.1 : 5 x 5 : Return of annually investment summary table.

\[\Re = \sum_{i=1}^{n}\rho_{i}^{EM}/\sum_{i=1}^{n}\rho_{i}^{BK}\] equation 4.1.1

\(\Re\) is the return rates of investment. The \(\rho_i^{EM}\) is the estimated probabilities which is the calculated by firm A from match 1,2… until \(n\) matches while \(\rho_{i}^{BK}\) is the net/pure probability (real odds) offer by bookmakers after we fit the equation 4.1.2 into equation 4.1.1.

\[\rho_i = P_i^{Lay} / (P_i^{Back} + P_i^{Lay})\] equation 4.1.2

\(P_i^{Back}\) and \(P_i^{Lay}\) is the backed and layed fair price offer by bookmakers.

We can simply apply equation above to get the value \(\Re\). From the table above we know that the EMPrice calculated by firm A invested at a threshold edge (price greater) 1.0769894, 1.1072203, 1.0781056, 1.1148426, 1.0671108 than the prices offer by bookmakers. There are some description about \(\Re\) on Dixon & Coles 1996. The optimal value of \(\rho_{i}\) (rEMProbB) will be calculated based on bootstrapping/resampling method in section [4.2 Kelly Model].

Table 4.1.2 : Probabilities Table
No EUPrice HKPrice fHKPriceL fMYPriceB fMYPriceL netProbB netProbL rEMProbB rEMProbL favNetProb undNetProb
2307 1.84 0.84 1.060 0.84 -0.943 0.4421 0.5579 0.476630 0.523370 0.4421 0.5579
826 1.60 0.60 1.280 0.60 -0.781 0.3191 0.6809 0.353314 0.646686 0.3191 0.6809
1501 1.88 0.88 1.000 0.88 1.000 0.4681 0.5319 0.504139 0.495861 0.5319 0.4681
9709 1.88 0.88 1.020 0.88 -0.980 0.4632 0.5368 0.516395 0.483605 0.4632 0.5368
1788 1.50 0.50 1.401 0.50 -0.714 0.2630 0.7370 0.283542 0.716458 0.7370 0.2630
8296 1.93 0.93 0.950 0.93 0.950 0.4947 0.5053 0.551513 0.448487 0.4947 0.5053

table 4.1.2 : 48640 x 45 : Odds price and probabilities sample table.

Above table list a part of sample odds prices and probabilities of soccer match \(i\) while \(n\) indicates the number of soccer matches. We can know the values rEMProbB, netProbB and so forth.

graph 4.1.1 : A sample graph about the relationship between the investmental probabilities -vs- bookmakers’ probabilities.

Graph above shows the probabilities calculated by firm A to back against real probabilities offered by bookmakers over 48640 soccer matches.

Now we look at the result of the soccer matches.

table 4.1.3 : 7 x 8 : Summary of betting results.

The table above summarize the stakes and return on soccer matches result.

[1] -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 [12] -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 [23] 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 [34] 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 [45] 7.50 7.75 8.00 8.25

4.2 Linear Model

From our understanding of staking, the covariates we need to consider should be only odds price since the handicap’s covariate has settled according to different handicap of EMOdds.

Again, I don’t pretend to know the correct ???odel, here I simply apply linear model to retrieve the value of EMOdds derived from stakes. The purpose of measure the edge overcame bookmakers’ vigorish is to know the levarage of the staking activities onto 1 unit edge of odds price by firm A to agency A.

## Test
## Choosing the variables of linear models
#'@ summary(lm(Return~HCap, data=dat))
#'@ summary(lm(Return~HKPrice, data=dat))
#'@ summary(lm(Return~HCap+HKPrice, data=dat))
#'@ summary(lm(Return~HCap+pHKRange, data=dat))
#'@ summary(lm(Return~ipRange, data=dat))
#'@ summary(lm(Return~ipHCap, data=dat))
#'@ summary(lm(Return~CurScore+ipHCap, data=dat))
#'@ summary(lm(Return~CurScore+ipRange, data=dat))
#'@ summary(lm(Return~CurScore+ipRange+ipHCap, data=dat))

## Choosing the variables of linear models
#'@ summary(lm(Stakes~HCap, data=dat))
#'@ summary(lm(Stakes~HKPrice, data=dat))
#'@ summary(lm(Stakes~HCap+HKPrice, data=dat))
#'@ summary(lm(Stakes~HCap+pHKRange, data=dat))
#'@ summary(lm(Stakes~ipRange, data=dat))
#'@ summary(lm(Stakes~ipHCap, data=dat))
#'@ summary(lm(Stakes~CurScore+ipHCap, data=dat))
#'@ summary(lm(Stakes~CurScore+ipRange, data=dat))
#'@ summary(lm(Stakes~CurScore+ipRange+ipHCap, data=dat))

## Linear Mixed Effects Models
#'@ library('lme4')
#'@ 
#'@

[15]John Fingleton & Patrick Waldron (1999) apply Shin’s model and finally conclude suggests that bookmakers in Ireland are infinitely risk-averse and balance their books. The authors cannot distinguish between inside information and operating costs, merely concluding that combined they account for up to 3.7% of turnover. They compare different versions of our model, using data from races in Ireland in 1993. The authors’ empirical results can be summarised as follows:

  • They reject the hypothesis that bookmakers behave in a riskneutral manner;
  • They cannot reject the hypothesis that they are infinitely riskaverse;
  • They estimate gross margins to be up to 4 per cent of total oncourse turnover; and
  • They estimate that 3.1 to 3.7% (by value) of all bets are placed by punters with inside information.

Here I try to test our data if there has any insider information.

4.3 Kelly Model

From the papers Niko Marttinen2001 and Jeffrey Alan Logan Snyder 2013 both applying Full-Kelly,Half-Kelly and also Quarter-Kelly models which similar with my previous Kelly-Criterion model englianhu2014 but enhanced.

To achieve the level of profitable betting, one must develop a correct money management procedure. The aim for a punter is to maximize the winnings and minimize the losses. If the punter is capable of predicting accurate probabilities for each match, the Kelly criterion has proven to work effectively in betting. It was named after an American economist John Kelly (1956) and originally designed for information transmission. The Kelly criterion is described below:

\[S=(\rho*\sigma-1)/(\sigma-1)\] equation-4.3.1

Where S = the stake expressed as a fraction of one’s total bankroll, \(\rho\) = probability of an event to take place, \(\sigma\) = odds for an event offered by the bookmaker. Three important properties, mentioned by Hausch and Ziemba (1994) (Efficiency of Racetrack Betting Markets (2008Edition)), arise when using this criterion to determine a proper stake for each bet:

  • It maximizes the asymptotic growth rate of capital

  • Asymptotically, it minimizes the expected time to reach a specified goal

  • It outperforms in the long run any other essentially different strategy almost surely

The criterion is known to economists and financial theorists by names such as the geometric mean maximizing portfolio strategy, the growth-optimal strategy, the capital growth criterion, etc. We will now show that Kelly betting will maximize the expected log utility for sports-book betting.

[1] 23.71528

\[K = \frac{(B + 1)p - 1} {B}\] equation 4.3.1

\[G: = \mathop {\lim }\limits_{N \to \infty } \frac{1/N}{\log}\left( {\frac{{{BR_N}}}{{{BR_0}}}} \right)\] equation 4.3.2

\[BR_N = (1 + K)^W(1 - K)^L BR_0\] equation 4.3.3

Kelly K-value ????????????????????????

## Bootstrapping to get the optimal value
#'@ llply(rEMProbB)

table 4.3.2

In order to get the optimal value, I apply the bootrapping and resampling method.

\[L(\rho) = \prod_{i=1}^{n} (x_{i}|\rho)\] equation 4.3.4

Now we look at abpve function from a different perspective by considering the observed values \(x1, x2, …, xn\) to be fixed parameters of this function, whereas \(\rho\) will be the function’s variable and allowed to vary freely; this function will be called the likelihood.

4.4 Poisson Modelling

Here we introduce the Dixon & Coles 1996 Poisson model and its codes. You are freely learning from below links if interest.

Source: local data frame [10,008 x 10]

              Date         Home         Away    HG    AG InPlay
            <time>       <fctr>       <fctr> <dbl> <dbl> <fctr>

1 2011-01-12 03:45:00 Huddersfield Huddersfield 0 0 No 2 2011-01-12 03:45:00 Torquay Torquay 0 0 No 3 2011-01-19 03:45:00 Aldershot Aldershot 0 0 No 4 2011-01-20 01:45:00 Twente Twente 0 0 No 5 2011-01-20 01:45:00 Twente Twente 0 0 No 6 2011-01-20 02:00:00 Koblenz Koblenz 0 0 No 7 2011-01-22 23:00:00 Arsenal Arsenal 0 0 No 8 2011-01-22 23:00:00 Arsenal Arsenal 0 0 No 9 2011-01-27 02:00:00 MSV Duisburg MSV Duisburg 0 0 No 10 2011-01-29 03:45:00 Millwall Millwall 0 0 No .. … … … … … … Variables not shown: InPlay2 , Mins , Mins2 , Picked2 .

Due to the soccer matches randomly getting from different leagues, and also not Bernoulli win-lose result but half win-lose etc as we see from above. Besides, there were mixed Pre-Games and also In-Play soccer matches and I filter-up the sample data to be 20009 x 45. I don’t pretend to know the correct answer or the model from firm A. However I take a sample presentation An introduction to football modelling at Smartodds from one of consultancy firm which is Dixon-Coles model and omitted the scoring process section.

Here I cannot reverse computing from barely \(\rho_i^{EM}\) without know the \(\lambda_{ij}\) and \(\gamma\) values. Therefore I try to using both Home and Away Scores to simulate and test to get the maximum likelihood \(\rho_i^{EM}\).

\[X_{ij} = pois(\gamma \alpha_{ij} \beta_{ij} ); Y_{ij} = pois(\alpha_{ij} \beta_{ij})\] equation 4.4.1

sample…

4.5 Staking Modelling and Money Management

sample… Geometric Mean

4.6 Expectation Maximization and Staking Simulation

sample…

5. Result

5.1 Comparison of the Results

Chapter 4.2 Comparison of Different Feature Sets and Betting Strategies in

Dixon&Pope2003 apply linear model to compare the efficiency of the odds prices offer by first three largest Firm A, B and C in UK.

5.2 Market Basket

Here I apply the arules and arulesViz packages to analyse the market basket of the bets.

6. Conclusion

6.1 Conclusion

Due to the data-sets I collected just one among all agents among couple sports-bookmakers 4lowin. Here I cannot determine if the sample data among the population…

JA: What skills and academic training (example: college courses) are valuable to sports statisticians? KW: I would say there are three sets of skills you need to be a successful sports statistician: - Quantitative skills - the statistical and mathematical techniques you’ll use to make sense of the data. Most kinds of coursework you’d find in an applied statistics program will be helpful. Regression methods, hypothesis testing, confidence intervals, inference, probability, ANOVA, multivariate analysis, linear and logistic models, clustering, time series, and data mining/machine learning would all be applicable. I’d include in this category designing charts, graphs, and other data visualizations to help present and communicate results. - Technical skills - learning one or more statistical software systems such as R/S-PLUS, SAS, SPSS, Stata, Matlab, etc. will give you the tools to apply quantitative skills in practice. Beyond that, the more self-reliant you are at extracting and manipulating your data directly, the more quickly you can explore your data and test ideas. So being adept with the technology you’re likely to encounter will help tremendously. Most of the information you’d be dealing with in sports statistics would be in a database, so learning SQL or another query language is important. In addition, mastering advanced spreadsheet skills such as pivot tables, macros, scripting, and chart customization would be useful. - Domain knowledge - truly understanding the sport you want to analyze professionally is critical to being successful. Knowing the rules of the game; studying how front offices operate; finding out how players are recruited, developed, and evaluated; and even just learning the jargon used within the industry will help you integrate into the organization. You’ll come to understand what problems are important to the GM and other decisionmakers, as well as what information is available, how it’s collected, what it means, and what its limitations are. Also, I recommend keeping up with the discussions in your sport’s analytic community so you know about the latest developments and what’s considered the state of the art in the public sphere. One of the great things about being a sports statistician is getting to follow your favorite websites and blogs as a legitimate part of your job!

source : Preparing for a Career as a Sports Statistician: Two Interviews with People in the Field

… … …

6.2 Future Works

I will be apply Shiny to write a dynamic website to utilise the function as web based apps. You are welcome to refer SHOW ME SHINY.

I will also write as a package to easier load and log.

7. Appendices

7.1 Documenting File Creation

It’s useful to record some information about how your file was created.

  • File creation date: 2015-07-22
  • R version 3.3.0 (2016-05-03)
  • R version (short form): 3.3.0
  • rmarkdown package version: 0.9.6
  • File version: 1.0.0
  • File latest updated date: 2016-06-22
  • Author Profile: ?????, Eng Lian Hu
  • GitHub: Source Code
  • Additional session information

[1] “2016-06-22 12:04:29 JST” setting value
version R version 3.3.0 (2016-05-03) system x86_64, mingw32
ui RTerm
language (EN)
collate English_United States.1252
tz Asia/Tokyo
date 2016-06-22
sysname release version nodename “Windows” “10 x64” “build 10586” “RSTUDIO-SCIBROK” machine login user effective_user “x86-64” “scibr” “scibr” “scibr”

7.2 Versions’ Log

  • File pre-release version: 0.9.0
    • file created
    • Applied ggplot2, ggthemes, directlabels packages for ploting. For example, the graphs applied in Section 2. Data.
  • File pre-release version: 0.9.1
    • Added Natural Language Analysis which is research for teams’ name filtering purpose.
    • Changed from knitr::kable to use datatble from DT::datatable to make the tables be dynamic.
    • Changed from ggplot2 relevant packages to googleVis package to make graph dynamic.
    • Completed chapter 3. Summarise the Staking Model.
  • File pre-release version: 0.9.2 - “2016-02-20 09:41:49 JST”
  • File version: 0.9.3 - “2016-02-05 05:24:35 EST”
    • Modified datatable to make the documents can be save as xls/csv
    • Added log file for version upgraded

7.3 Speech and Blooper

Firstly I do appreciate those who shade me a light on my research. Meanwhile I do happy and learn from the research.

There are quite some errors when I knit HTML:

  • let say always stuck (which is not response and consider as completed) at 29%. I tried couple times while sometimes prompt me different errors (upgrade Droplet to larger RAM memory space doesn’t helps) and eventually apply rm() and gc() to remove the object after use and also clear the memory space.

  • Need to reload the package suppressAll(library('networkD3')) which in chunk decission-tree-A prior to apply function simpleNetwork while I load it in chunk libs at the beginning of the section 1. Otherwise cannot found that particlar function.

7.4 References

Reference for industry knowdelege and academic research portion for the paper.

  1. () - Creating a Profitable Betting Strategy for Football by Using Statistical Modelling
  2. () - What Actually Wins Soccer Matches: Prediction of the 2011-2012 Premier League for Fun and Profit
  3. () - The value of statistical forecasts in the UK association football betting market
  4. () - Dixon and Cole’s Poisson regression R Packages
  5. () - Apply Kelly-Criterion on English Soccer 2011/2012 and () - Apply Kelly-Criterion on English Soccer 2012/2013
  6. () - An introduction to football modelling at Smartodds
  7. () - The Betting Machine
  8. () - The Kelly Criterion in Blackjack Sports Betting, and the Stock Market
  9. Fabián Enrique Moya (2012) - Statistical Methodology for Profitable Sports Gambling
  10. () - How to apply the Kelly criterion when expected return may be negative?
  11. () - Money Management Using The Kelly Criterion
  12. () - Optimal Exchange Betting Strategy For WIN-DRAW-LOSS Markets
  13. () - Kelly criterion with more than two outcomes
  14. () - ????????????????????????
  15. John Fingleton & Patrick Waldron (1999) - Optimal Determination of Bookmakers’ Betting Odds: Theory and Tests
  16. Maurizio Montone (2015) - Optimal Pricing in the Online Betting Market
  17. Steven D. Levitt (2004) - Why are Gambling Markets Organised so Differently from Financial Markets?
  18. Steven Xu (2013) - Forecasting Accuracy and Line Changes in the NFL and College Football Betting Markets
  19. Kwinten Derave (2013-2014) - The Forecast Ability of the Dispersion of Bookmaker Odds

Reference for technical research on programming and coding portion for the paper.

  1. () - Wrangling F1 Data With R
  2. () - Interactive visualizations with R - a minireview
  3. () - R + htmlwidgets + DT + sparkline

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